Answer:
[tex]\displaystyle \int\limits^e_1 {\frac{8}{x}} \, dx = 8[/tex]
General Formulas and Concepts:
Calculus
Integration
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^e_1 {\frac{8}{x}} \, dx[/tex]
Step 2: Integrate
- [Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^e_1 {\frac{8}{x}} \, dx = 8\int\limits^e_1 {\frac{1}{x}} \, dx[/tex]
- [Integral] Logarithmic Integration: [tex]\displaystyle \int\limits^e_1 {\frac{8}{x}} \, dx = 8 \ln |x| \bigg| \limits^e_1[/tex]
- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^e_1 {\frac{8}{x}} \, dx = 8[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
